The commutant of L_\widehat\fraksl₂(n,0) in the vertex operator algebra L_\widehat\fraksl₂(1,0)^{⊗ n}

2013/11/04 by Cuipo, Jiang, Zongzhu Lin +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Quantum Algebra(math. QA) #Representation theory (math. RT) #math.QA

paper · pdf · doi:10.48550/arxiv.1311.0608

28 pages

arxiv created 2013/11/04 · openalex publication_date 2013/11/04 · arxiv updated 2013/11/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We study the commutant L_\widehat\fraksl₂(n,0)^c of L_\widehat\fraksl₂(n,0) in the vertex operator algebra L_\widehat\fraksl₂(1,0)^{⊗ n}, for n≥ 2. The main results include a complete classification of all irreducible L_\widehat\fraksl₂(n,0)^c-modules and a proof that L_\widehat\fraksl₂(n,0)^c is a rational vertex operator algebra. As a consequence, every irreducible L_\widehat\fraksl₂(n,0)^c-module arises from the coset construction as conjectured in \citeLS.

Cited by

• Representations of the parafermion vertex operator algebras
• Commutant of L_\widehat\mathfraksl₂(4,0) in the cyclic permutation orbifold of L_\widehat\mathfraksl₂(1,0)^{⊗ 4}

Related

• Structure and representations of the coset vertex operator algebra C( L_\widehatosp(1|2)(2,0), L_\widehatosp(1|2)(1,0)^{⊗ 2})
• Coset Vertex Operator Algebras and \W-Algebras
• Commutant of L_\widehat\mathfraksl₂(4,0) in the cyclic permutation orbifold of L_\widehat\mathfraksl₂(1,0)^{⊗ 4}
• Vertex operator algebras associated to admissible representations of sl₂
• Rationality and C₂-cofiniteness of certain diagonal coset vertex operator algebras